The Widget Manufacturing Company makes two products, Alpha Widgets and Beta Widgets. Each Alpha Widget gives a profit of $3, while each Beta Widget earns $7. The company must manufacture at least one Alpha Widget per day to satisfy its customers, but no more than five because of the number of employees needed to create the item. Also, the number of Beta Widgets produced cannot exceed six per day. As a further constraint, Alpha Widgets cannot exceed the number of Beta Widgets. How many of each Widget should the company produce in order to obtain the maximum profit?